Eigenvectors keep their direction under a matrix
This animation shows a linear transformation acting on the plane, with a grid of vectors sweeping and stretching under the map. Before the transformation is applied, two special vectors are highlighted in a distinct color to show they define the only directions that remain unrotated, only scaled. Paced with clear timing beats, it helps students build intuition for eigenvectors and eigenvalues before diving into matrix computations.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Apply ALL of the following review notes precisely; keep everything else identical. This video is for social media and must be impeccable. - I would highlight the two vectors that will not turn before applying the transformation
Make the next one in this series
- Show how eigenvalues determine whether the highlighted eigenvectors stretch, shrink, or flip direction
- Animate a 3x3 matrix transformation in 3D and highlight its eigenvector axes
- Compare a shear transformation with no real eigenvectors to a stretch with two real eigenvectors
